Electrical analyzer for 45 u deg. strain rosette data



194. s. s. MANSON 2,447,517

ELECTRICAL ANALYZER FOR 45 STRAIN ROSETTE DATA 2 Sheets-Sheet 1 Filed March 12, 1945 Aug; 24 W48.

ELECTRICAL ANALYZER FOR 45 STRAIN ROSE'I'TE DATA Filed March 12, 1945 2 Sheets-Sheet 2 SAMUEL S. MANSON I Three knobs,

Patented Aug. 24, 1948 UNITED STATES PATENT; OFFICE ELECTRICAL- ANALYZER non 45 mm aosn'rra DATA I Samuel S. Manson, Cleveland,, Ohio Application March 12, 1945, Serial No. 582,371

' 2 Claims. (01. 235-61) (Granted under the act of March amendedApril'30, 1928; 3'70 0.

This invention relates to "an electric analyzer for 45 strain rosette data for computing the maximum shear strain and major and minor principal strains from a 45 strain rosette consisting of only three gages, 45 and 90 apart, mounted at selected points on a thin wall stressed surface structure.

The object of this invention is to provide a simple calculator that obviates the use of mechanically trained personnel in a fraction of the time required by any known long hand method.

Another object of this invention is to provide a cheap, compact, portable and easily assembled computer arrangement of standard electrical elements. v

The objects are attained by mechanism illustrated in the accompanying drawings, in which:

Fig. 1 is a front view of the panel of the analyzer of this invention; I I

Fig.2 is a front view of the power section shown in connected relationship with Fig. 1;

Fig. 3 is .a circuit diagram of the analyzer of this invention divided in, 3a, the panel section. 3b, the cathode ray tube, and 3c, the power circuits;

Fig. 4 shows the resolution of voltage Elie of Fig. 3;

, Fig. 5 shows the resolution of voltage End of Fig. 3; and Fig. 6 is the vector addition of Eon and Eric.

The following symbols are used throughout; E1, E2 and E representthe observed strained indications on gages (not shown), one, two and three, respectively, of a 45- strain rosette. Gage l is the reference gage and gages two and three are oriented respectively, at 45 and 90 positive, counterclockwise to gage I. Ep and P1; are the major and minor principal strains at the point of the surface of test in microinches per inch.

-Y max. represents the maximum shear strain at the point of surface under test in microlnches per inch; 6;, is the angle of major principal axis in degrees measured position counterclockwise from the reference gage l ofthe rosette (not shown). 10, H, II, for setting the input strains from the rosette, are shown in Fig. 1. These knobs actuate voltage taps on potentiometers' l3, l4, (Fig, 3), placed across a 60- cycle input line.- Rotating the knobs clockwise introduces voltages into the analyzer representing positive strains. Similarly, a counterclockwise movement represents negative strains. 7 These settings are indicated by a mic-roammeter It.

A master selective switch I1 is provided for denoting the quantitybeing indicated by the meter I6.

3, 1883, as G. 757) This switch l'l' consists of five of the six-positioned selector switches ganged together on a common shaft. Two polarity reversing switches l8, 9 are provided which require initial adjustment. The strainsEi and E3 arecompared and if the larger arithmetical of the two is positive, the-E1 plus E3 switch I9 is turned to the plus position, while if-the larger is negative, the switch is turned to the minus position. wThis switch is merely a reversing control, and consequently, switching a selector to positive causes current to pass in a position direction through the meter. Likewise. a reversing switch l8 for the meter is also provided, and its purpose is to indicate whether the principal stresses are-positive or negative. Three scales are marked on the meter l6, .0 to 100, 0 to 200 and 0 to 500', whichpermit meter lBto be used over much wider range. Shunts for reducing the meter curent for one half and one fifth arealso provided by a knob 20. In some problems, the choice of a scale which permits the meter to be used at a fair portion of its range in the setting of E1, E2 and E3, results in a determination of maximum shear or principal strain larger than the maximum value of the indicator scale, shown'at Hi. When this occurs, these shunting switches are introduced and compensated for by multiplying the meter reading by 'two orfive, depending on the scale factor used.

Indication of the orientation of the major principal axes is accomplished by means of a cathode ray tube oscillograph 2|, the screen 22 of which is covered with a .calibrated radial line scale, best shown in Fig. 1. After the settings for the three strains, E1, E2 and Ea from the rosette have been adjusted, a straight line is found to appear on the oscillograph. screen, 2 2. This line passes through the origin, a portion on one side ofthe origin being longer than the portion on the other side, the shorter part being tapered at its end while the longer isof uniform width through its length with abright spot at'its extremity. This longer line points to a scale value which indicates the direction of the major principal axes with reference to gage lineof the rosette (not shown). The cathode raytube 2| acts as a ratio meter and indicates theratioof the voltages which in turn determine the orientation ofthe major axes. The principal components of the electrical circuit of Fig. 3 are the strain setting potentiometers l3, l4, l5, resistor-condenser combinations and two diode rectifiers 23, 24. The resistor-condenser combinations rotate the phase of 'voltages by the taps of the potentiometer so that the 'vector sums ofqcombinations of these voltages meter polarity I8 is switched to plus as it should.

always be at the beginning of any analysis, since the larger of E1 and E3 is negative, the El plus'E'q toggle I9 is switched to minus. The meter range to 500 is apparently most suitable and is sistently used throughout the analysis. Switch is brought to the one position, 'themasterselector switch I! is brought to the E1, position, and the dial ID for E1 is turned clockwise until the meter l6 reads 150. With themaster selectorswitch I! in the E2 position, the E2 dial H is turned clockwise until the meter I 6 reads 200. With the masterswitch I 1. in the E3 position, the dial I! for E3 is turned countereclockwise until the meter-reads250. The. cathode ray oscillo.-. graph H is examined and it appears that the iarger portion of the. line through the origin points to a value equalto 26* on scale l2. The master selector I1 is turned to the Y max. position. The meter pointer t6. isobservedto. be off scale so that scale factor switch 20. is turned to two. The meter i6 reading is320, hence, two times320. equal 640 nucroinches per inch. The master selector I1 is turned to Ep, the meter It reads. 275, :when the. meter factor 28 is returned to unity. Hence E12 equals 275 .microinches per inch. The master selector H: is turned to Eq. the meter is reads oif scale 'tothe left so its polarity issw-itched byti8 to minus. The meter [6 reads 370; hence Eq8quaJSmiHl1S370 microinches per inch. The accuracy of the reading is deter-mined to be in the neighborhood of 2%. full scale. Slime ilarly, the ang-ularity is indicated correctly to twodegrees.

The ry annotation The electrical circuit of the analyze was .1 siened to compute. io a straightforward iashion, the indi idual quantities ap earin in the f rmuiasxfaestrain. and subsequently. to c mb ne theseauantities to yield final strain and. h ir orientations. From Brecht. a k. Pho Elasticity. volume -1, John. Wiley ace ficns. Inv- Wenote that.

Yes. equals fla are-( ar (1) across-a common 60 cycle A; C. line. Inoperacan, thetaps A, C. and are displaced from the electricaloen'ters O of the potentiometers by distances proportional to E1, E2 and E3, respectively.

Thus, the A. G. voltage between A and C is proportional to'(E2'E1) and the voltage between G and proportional to (sa -s3); These. two

voltages are placed across impedances consisting of a condenser and a resistor, each condenser being chosen to have capacitive reactance, at the imposed frequencies of 60 cycles, equal to the resistances with which it is connected in series. From Fig. 3, the voltage across the resistor BC is thus equal to where EAc is the voltage between A and C and it leads EAC by The voltage across CE is qualaudit lags another EcF by 45. Now Eco and Eon are in phase since they are derived through resistances; from a common A. C. source. Hence,

the voltage across BC leads the voltage across CE by Since thesetwo voltages are proporticnalrc izect v l t v (7E2 E1). and. le-E3) It follows that the voltage EBB is just half of the desired maximum shear strain. The factor of 2 is talgen into account in the metering ofthis voltage, Referring to Fig. 3;, the process of setting the strains E1, E2 and E3 consists of moving the taps of the rheostat Potentiometers i3. l4 and 1'5 until the desired readings are obtained on a voltmeter which is successivelyconnected; by means of a switch between the taps and a fixed point on the reierenceresistor 29. The volt meter consists ofa'D. G. microammeter l6, a diode rectifier 24 and a large series dropping resistor38.- When the master electrical switch is in the Y max. position, the same voltmeter-measures the voltage between B- and E. It'is merely necessary to reduce the metering resistance to half its; value when measuring the shear strain and the meter; will indicate the full magnitude of", the maximum shear strain.

Major and minor principal.- strains; j Elie e re ion for themaiqr principal strain. is

.to the same-shaft, and. rotated by the same knob i211 However; their inputs-from; the 6,0;cycle line fillQgCliQSSfillg'SQfihfigl-i as the knob; I2 is rotated, one tap Emotes toward on of. the i put i es,- h .otheretan H moves, equalamount toward the otheminnutplinc. t e. ol a e; b w en A and iiis prceqrti cel. t0.- ;+E h vo ta e is pla ed; across two c st r BG and. G. d

two. conde sers an Th to l capac tive neactance is -v e s eons; i chosen qual. to the total resistance; hence, the voltage total resistance, EBG, is equal to across" the which in turn is equal to 5 L2 i-l' a) is again taken care of by adjusting the resistance of the circuit measuring this voltage.

When the master selector switch is in the position for measuring Ep, both the voltages representing the expressions in Equation 2 feed current through the microammeter IS. The currents due to these voltages are not in phase, however, and if they were added without regard to phase shift, the sum would be a vector sum, and not the scalar sum as required by Equation 2. The expedient used for taking into account the phase difierence is the process of rectification. Each of the two currents is independently rectified before it enters the meter IS. The currentin the meter thus consists of two D. C. components, each proportional to one of the expressions in Equation 2, plus numerous harmonics which do not activate the direct current meter. The D. C. components, which do activate the meter I6 are in essence in phase, and, therefore, add in scalar form to yield a net result indicating the major principal strain: The direction in which the current due to (E1+E3) flows through the meter depends upon the orientation of the rectifier 23. Hence, a polarity switch for (E1+E3) is provided. When the I, switch is in the plus position, current flows in positive fashion. It is left to the operator to perform the switching operation. Y

The expression for the minor principal strain is identical with that previously given in Equation 2, except that the sign preceding the square root portion is negative. To obtain the minor principal strain, it is necessary onlyto reverse the rectifier of the portion feeding current due to the square root expression.

Direction of major principal axes The angle of the major principal axes measured positive counterclockwise from the direction of gage l is If, then, a means were devised for indicating the ratio of (E2E3) to (Ea-E1), this ratio would define a function of 0 which in turn would determine 0 Two voltages representing (Ea-E1) and (Ea-E3) are present between CA and CF respectively (Fig. 3). These two voltages are in phase, and they vary sinusoidally with time. If they are impressed across the horizontal and vertical I plates of a cathode ray oscillograph 2|, the horiis the desired ratio.

6 zontal and vertical displacements, Kr and Ye, at any time, t,- of the cathode beam are where K is the deflection sensitivities of both sets of plates in inches per volt, and f is the impressed frequency of 60 cycles per second.

Dividing the Equation 6 by the Equation '7,

Thus the path traced by the cathode ray spot is a straight'line through the origin whose slope The straight line, in conjunction with a radial scale, then indicates 01;. A convenient method of determining the radial scale is to assume consecutive values of 0 and to determine'from Equation 5 the ratio that corresponds to each value of 0 A straight line is seen extending in both directions through the origin points to two angles, one at each end of the line. This ambiguity of angle is due to the fact that the value of the tangent of an-angle does not in itself uniquely define the angle. The tangent must be considered as a frac: tion and the signs of the numerator and denominator must'be examined individually in order to determine the quadrant in which the angle lies, and thus the valu of the angle itself. The problem is to determine not only the polarity relation between (Ez-E1) and (Ea-E3) but also the absolute polarity of each of these quantities, taking the voltage input to the system as reference. By using the latter voltage to modulate the beam of the oscillograph 2|, this polarity may be taken into account. In Fig. 3, it is seen that the control grid circuit of the cathode ray tube contains a transformer driven from the input line. The transformer is chosen to bias the grid beyond cut-off at the negative peak of the input cycle, thus removing the beam from the screen during a portion of the cycle. The undiminished line then points to a unique value of 0p on the scale. Of course, it is necessary to position the scale and the screen in such a manner that the proper value of 0p is indicated. I

Stresses It is possible to devise an analyzer to compute stress instead of strain. The formulas for maximum shear stress and principal stresses contain the same strain combinations, (EH-E3) and (V (E2E1) +(E2-Es) as those appearing in the formulas for strain but the coefficients of these equations contain themodulus of elasticity and Poissons ratio of the material under test.

To convert the strain analyzer to a stress computer, itis only necessary to change the values of the metering resistances, and to add scales on the meter for stress. The same instrument may be made to indicate both stress and strain by the use of a toggle selector switch, or two meters may be provided, one indicating strain, the other stress.

Fig. 3 shows three identical condensers, 32, 33, 3A, of 0.5 microfarad, each matched with identical resistors 35, 36, 31, of 5,000 ohms. Actually it is not important that the condensers and resistors be identical; but the accuracy of the instrument is greatly afiected by the closeness of the match between each condenser and its particular re sistance. Thus, three arbitrary condensers of a r-came nominal dimicroiaradsizemay 'be chosemfand each in turn placed in series. with a. 6Q cycle .voltage source and a variable resistor. The resistance then variedluntilth.measured voltage across itis equal to the measured voltage across the condenser-.- The proper resistance for each-condenser is-"thuadetermineda The operation of setting the strains Er, E2 and Eainto the instrument consists ofmoving the taps A, C and F of the various. potentiometers to points of; potential corresponding to the strains. The reference potential'is that of a fixed point in a resistor-placed across the input line... Normally, thisrreierence point 0 wouldnot be. 'uni ue and any point approximately: half way-between the two-input lineswould be a satisfactory reference. Because the operation-of the instrument depends, however. on the fact that for anyposition oi the dial for E3, the tap of one of the coupled potentiometers is as far above the reference point as the tap of the otherpotentiometer is below it, it follows that there is only one point in the reference resistor which maybetaken as the reference potential. To obtain this point, a sensitive voltmeter is first placed between the taps of the coupled potentiometer E on the his shaft, and the E3 dial is rotated until the voltmeter reads zero. The voltmeter is then connected between one of the E: taps and a tap on the reference resistor, and the latter tap is adjusted for a zero reading of the voltmeter. The position .Of the tap on the reference resistance thus determined, is. the reference potentialof the instrument.

The metering resistance 38 is arbitrarily chosen so, as to provide full scale deflection of the meter for the full range of the E1, E2 and E3 dials. The other two metering resistances 39 and 35 arebest determined'by experiment, since their theoretical values are somewhat obscured by the presence of rectifiers 23, 24. If, for instance, E1 and E3 are set equal to zero. and E2 set. to an arbitrary value, then the meter reading, when the master selector switch is set to the Y position,.should be twice the value of E2. The resistance 39 is determined by varying its value until this condition prevails... Also, if E1, E2 and E3 are all set to arbitrary equal values, then the reading of the meter when the master selector switch is in the Ep position, should be equal torthe arbitrary value of E1... E2: and E3. Resistance 3! is adjusted until this condition prevails.

When a diode rectifier 23 is placed in a relat ively low-impedance circuit a small current is found to flow in the circuit even when no external voltage is applied. This phenomenon is due to the fact that emission takes place from the cathode, and some electrons find their way to the plate even when the plate is not positively charged. One expedient for reducing the current flow at zero applied voltage is to reduce the temperature of the cathode. For a 6H6 diode 23- the normal filament voltage is 6.3 volts. It was found that approximatelyBj volts to the filament provided adequate temperature to permit a. full-scale current of I00 microamperes to flow, and at the same time the temperature was low enough to prevent undesirable. emission. The filament voltage is reduced by center-tapping a 6.3 volts filament transformer.

' Equations 6 and 7 for horizontal and vertical displacements are validonly if the deflection sensitivities of the vertical and horizontal plates are equal. Because of manufacturing tolerances in the cathode ray tube 2 l, the sensitivities may not be'identical; hence resistorgain controls are pro vided for adjusting them to equality.

The most convenient manner of adjusting the angular scale into its proper position relative to the screen 22, of the cathode ray tube 2| is to orient the screen and scale until the principal angle indication is correct for at least one combination of E1, E2 and E3. Then it is positioned correctly for all other combinations of rosette strains. It is desirable to fix the scale so that the zero direction is vertical. Irf E2 is set equal to zero, E1 to positive full scale and E3 to negative full scale, the resulting. principal angle indication should be zero degrees. The screen 22 is rotated. until the line on it points to the. zero deree mark on the scale.

While, this invention has been described in conjunction with the following value of components, itshould beexpressly understood that. various changesmas be made without departing. from the spirit'o'f the invention, as defined in the appended claims.

29:300 50 w; adjustable tap 323; 14,15, 30:300 50 w. rheostat potential.

36, 37=5000. 2 w. wire wound 3'8=l30,060 1 w. wire wound 39:65.060 1 w. wire wound 3l-=I85,000 1 w. wire wound lo-AMEN 4 w. wire wound While Fig. 1 and Fig. 2 are shown separated by a -cablethey could be combined in one cabinet if desirable.

The mvention described herein may be manufacturedrand used by or for the Government of the United States of America for governmental purposes'wlthout the payment of any royalties thereon or therefor.

What is claimed is:

u 1. In an. electric circuit for determining characteristic data about a. stress: point on the surface oi.a..-thin walled structure to which a rosette isapplied consisting of three strain gages mount.- ed at. WAS", and 9!) about said point: for providing inaccordancewith said stresses; a source of alternating current, a pair oflines' connected to-said. source. four potentiometers connected in parallel across said lines and having a center reference. point, a movable contact on eaclrof said potentiometers controlled by one of three knobs, each knob being connected for moving the contact on one of said potentiometers for adjusting it withv respect to the corresponding center reference point in accordance with the signals obtained from the three. strain gages respeotively, the fourth contact being moved simultaneously acorresponding amount by the third knob in the opposite direction from its center reference point, a :branch comprising a reactance and a resistance, of equal magnitude at the frequency of the alterating current used, connected in series between the first and second contacts, another'similar. branch between the second and third contacts;- a third bran-ch having similar elements, reversed, between the second and fourth contacts, means including a multi-position switch .for indicating the. combined potential across .the resistance of said first branch and the reactance ofsaidsecond branch in one position of said switcfl1',calibrated.to show the value ofv the maximum shear strain. and .for indicating the scalar sum =01. the above-combined potential and the potentials across the resistances of the first and third branches in another position of said switch, said sum being calibrated to show the value of the major principal strain, and the scalar differenoe between said potential and the sum of the other two potentials to show the value of the minor principal strain, said means including a cathode day oscillograph having a radial scale and means for impressing the potentials across the first and second branches on the normally positioned pairs of plates respectively in said oscillograph, whereby the angle of the major principal axis will be indicated on the radial scale by the resultant trace.

2. In an electric circuit for determining characteristic data about a stress point on a surface to which a rosette has been applied, consisting of strain gages mounted at difierent relative angular relations about said point, a series of potentiometers connected in parallel across a source of alternating current, means for adjusting movable contacts along three of said potentiometers in accordance with the readings obtained from REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 2,375,227 Hillman May 8, 1945 2,382,994 Holden Aug. 21, 1945 2,385,334 Davey Sept. 25, 1945 

